Question 1

A firm has PVGO of 0 and a market capitalization rate of 12%. What is the firm's P/E ratio?

Accepted Answer

P = E/k + 0; P/E = 1/0.12 = 8.33

Question 2

The EBIT of a firm is $300, the tax rate is 35%, the depreciation is $20, capital expenditures are $60, and the increase in net working capital is $30. What is the free cash flow to the firm?

Accepted Answer

FCFF = 300(1 − 0.35) + 20 − 60 − 30 = $125 million

Question 3

A firm reports EBIT of $100 million. The income statement shows depreciation of $20 million. If the tax rate is 35% and total capital expenditures and increases in working capital total $10 million, what is the free cash flow to the firm?

Accepted Answer

FCFF = 100(1 − 0.35) + 20 − 10 = $75 million

Question 4

The free cash flow to the firm is reported as $405 million. The interest expense to the firm is $76 million. If the tax rate is 35% and the net debt of the firm increased by $50 million, what is the free cash flow to the equity holders of the firm?

Accepted Answer

FCFE = 405 − 76(1 − 0.35) + 50 = 405.6

Question 5

ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock.
What is the present value of growth opportunities for ART?

Accepted Answer

P₀ = 11eaaae8_8b53_5449_a4b8_c3c79034fcd2_TB6474_11 = 34.29 PVGO = P0 - (EPS1/k) = 34.29 - (3/.12) = $9.29

Question 6

Transportation stocks currently provide an expected rate of return of 15%. TTT, a large transportation company, will pay a year-end dividend of $3 per share. If the stock is selling at $60 per share, what must be the market's expectation of the constant-growth rate of TTT dividends?

Accepted Answer

k = D₁/P0 + g 0.15 = 3/60 + g g = 0.10

Question 7

ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock.
At what price would you expect ART to sell?

Accepted Answer

P₀= 11eaaae8_8b53_2d37_a4b8_d5f3e541d3dc_TB6474_11 = 34.29

Question 8

ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock.
At what P/E ratio would you expect ART to sell?

Accepted Answer

P₀ = 11eaaae8_8b53_2d38_a4b8_4f8587331946_TB6474_11 = 34.29 P/E = 34.29/3 = 11.43

Question 9

The free cash flow to the firm is reported as $275 million. The interest expense to the firm is $60 million. If the tax rate is 35% and the net debt of the firm increased by $33 million, what is the free cash flow to the equity holders of the firm?

Accepted Answer

FCFE = 275 − 60(1 − 0.35) + 33 = 269

Question 10

A common stock pays an annual dividend per share of $1.80. The risk-free rate is 5%, and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $1.80 per share, what is the value of the stock?

Accepted Answer

P = $1.80/0.09 = $20

Question 11

The free cash flow to the firm is reported as $198 million. The interest expense to the firm is $15 million. If the tax rate is 35% and the net debt of the firm increased by $20 million, what is the approximate market value of the firm if the FCFE grows at 3% and the cost of equity is 14%?

Accepted Answer

FCFE = 198 − 15(1 − 0.35) + 20 = 208.25
Value = (208.25 × 1.03)/(0.14 − 0.03) = 1,950

Question 12

Firm A has a stock price of $35, and 60% of the value of the stock is in the form of PVGO. Firm B also has a stock price of $35, but only 20% of the value of stock B is in the form of PVGO. We know that:
I. Stock A will give us a higher return than Stock B.
II. An investment in stock A is probably riskier than an investment in stock B.
III. Stock A has higher forecast earnings growth than stock B.

Accepted Answer

II and III onlyPVGO (Present Value of Growth Opportunities) indicates the portion of a stock's price that is attributed to future growth opportunities. A higher PVGO percentage (as in Stock A) suggests higher expected growth, making Statement III correct. Higher growth often comes with higher risk, making Statement II correct. Statement I is not necessarily true because a higher return is not guaranteed by a higher PVGO percentage alone; it also depends on how those growth opportunities materialize and other factors.

Question 13

A firm has a stock price of $54.75 per share. The firm's earnings are $75 million, and the firm has 20 million shares outstanding. The firm has an ROE of 15% and a plowback of 65%. What is the firm's PEG ratio?

Accepted Answer

EPS = $75,000,000/20,000,000 = $3.75
P/E = $54.75/$3.75 = 14.6
g = 0.65 × 15% = 0.0975 = 9.75%
PEG = 14.6/9.75 = 1.5

Question 14

ART has come out with a new and improved product. As a result, the firm projects an ROE of 25%, and it will maintain a plowback ratio of 0.20. Its earnings this year will be $3 per share. Investors expect a 12% rate of return on the stock.
What price do you expect ART shares to sell for in 4 years?

Accepted Answer

P₀ = 11eaaae8_8b53_544a_a4b8_8534f5e54718_TB6474_11 = 34.29 P₃ = P₀(1 + g)4 = 34.29(1.05)4 = 41.68

Question 15

A firm has an earnings retention ratio of 40%. The stock has a market capitalization rate of 15% and an ROE of 18%. What is the stock's P/E ratio?

Accepted Answer

11eaaae8_8b52_b801_a4b8_2fcd72785668_TB6474_11 = 11eaaae8_8b52_b802_a4b8_43b8e2f748cc_TB6474_11 = 7.69

Question 16

A firm increases its dividend plowback ratio. All else equal, you know that ________.

Accepted Answer

11eaaae8_8b53_0625_a4b8_c74eea966d8c_TB6474_11 = 11eaaae8_8b53_0626_a4b8_1bf2acb0e74c_TB6474_11

Question 17

The free cash flow to the firm is reported as $205 million. The interest expense to the firm is $22 million. If the tax rate is 35% and the net debt of the firm increased by $25 million, what is the approximate market value of the firm if the FCFE grows at 2% and the cost of equity is 11%?

Accepted Answer

FCFE = 205 − 22(1 − 0.35) + 25 = 215.70
Value = (215.7 × 1.02)/(0.11 − 0.02) = 2,445

Question 18

A stock is priced at $45 per share. The stock has earnings per share of $3 and a market capitalization rate of 14%. What is the stock's PVGO?

Accepted Answer

P₀ = 11eaaae8_8b52_df13_a4b8_11afafaa2f2b_TB6474_11 = PVGO; $45 - 11eaaae8_8b52_df14_a4b8_11bd9be17742_TB6474_11 = $23.57

Question 19

If a firm has a free cash flow equal to $50 million and that cash flow is expected to grow at 3% forever, what is the total firm value given a WACC of 9.5%?

Accepted Answer

Total value = 50/(0.095 − 0.03) = 769.23

Question 20

The free cash flow to the firm is $300 million in perpetuity, the cost of equity equals 14%, and the WACC is 10%. If the market value of the debt is $1 billion, what is the value of the equity using the free cash flow valuation approach?

Accepted Answer

Total value = 300/0.10 = $3 billion
Equity value = $3 billion − 1 billion = $2 billion

Quiz 13: Equity Valuation